@Kendama @miraja I have no real argument with those points. I do agree that there are some definite political reasons
not to do her in, which may outweigh the reasons
to do her in. Although when it comes to the starting-your-reign-with-an-act-of-clemency thing, I think it's worth noting that Yona isn't the queen yet (and in theory may never be, although I don't see who else around would make a workable successor when Soo-Won snuffs it). Nonetheless, whacking her could indeed potentially pull Kouka's relationship with the empire deeper into conflict.
And yeah, they don't know she's a serious hand-to-hand fighter. But still, I think both Soo-Won and Yona are underestimating her even in terms of what they know. In a milieu where there are plenty of serious badasses, who can be expected to be very difficult to stop from pursuing their agendas, her personality makes it clear that she is one of them. That woman is obviously not the kind of person you can expect to stick in jail with average jailers and have her be safely neutralized--whether she'll bust out, start pulling strings from where she is, smuggle messages out or whatever, you know she'll manage to do
something if you've been paying attention to her at all.
There's also the "Gollum" argument for letting her live.